Since the conception of magnetic resonance imaging (MRI) in 1973, a major driving force of its further technical, scientific and clinical development is the quest for speed. Historically, it took more than a decade before the fast low-angle shot (FLASH) MRI technique (DE 3 504 734 or U.S. Pat. No. 4,707,658 A) reduced the acquisition times for a cross-sectional image to the order of one second and allowed a continuous imaging due to the generation of a sufficiently strong steady-state MRI signal. Nevertheless, the monitoring of dynamic processes in real time remained hampered for two reasons: the need for still relatively long measuring times of several hundreds of milliseconds for images with a reasonable spatial resolution and the use of Cartesian encoding schemes that sample the MRI data space (k-space) on a rectilinear grid. Cartesian sampling refers to the acquisition of parallel lines in k-space and was preferred because of its tolerance to instrumental imperfections of early MRI systems and the simple reconstruction of an image by inverse fast Fourier transformation (FFT) of the raw data. Despite these advantages for static images, the continuous monitoring of a moving object is better served with radial encoding schemes as the information content of an individual “spoke” in k-space is of equal importance for the reconstructed image. This is due to the fact that each spoke, but not each parallel line, crosses the center of k-space and therefore contributes both high and low spatial frequencies. Only the latter determine the gross image content such as the position of a moving object.
On the other hand, the use of high-speed acquisition techniques for realtime MRI suffers from a number of specific drawbacks. For example, so-called single-shot gradient-echo sequences such as echo-planar imaging (P. Mansfield et al. in “J. Magn. Reson.” vol. 29, 1978, p. 355-373; and in “Br. Med. Bull.” vol. 40, 1984, p. 187-190) and spiral imaging (C. B. Ahnet al. in “IEEE Trans. Med. Imag.” vol. 5, 1986, p. 2-7; and C. H. Meyer et al. in “Magn. Reson. Med.” vol. 28, 1992, p. 202-213) are prone to geometric distortions or even local signal losses that are caused by their inherent sensitivity to off-resonance effects, tissue susceptibility differences, and magnetic field inhomogeneities, which are unavoidable in many parts of the body. Complementary, single-shot MRI sequences that employ radiofrequency-refocused spin echoes (J. Hennig et al. in “Magn. Reson. Med.” vol. 3, 1986, p. 823-833) or stimulated echoes (J. Frahm et al. in “J. Magn. Reson.” vol. 65, 1985, P. 130-135) and therefore are free from such problems, lead to a pronounced radiofrequency power absorption with the risk of local tissue heating or suffer from a compromised signal-to-noise ratio, respectively.
An essential improvement for MR imaging in real time has been obtained with a combination of fast low-angle shot MRI sequences (FLASH sequences) with radial data sampling and view sharing of successive raw data acquisitions (see S. Zhang et al. in “Journal of magnetic resonance imaging”, Vol. 31, 2010, p. 101-109). The radial data sampling allows a moderate undersampling factor (about 2) resulting in an image raw data acquisition of about 250 ms per frame. With a reconstruction of image updates using current image raw data of a part of a frame and preceding image raw data (so-called sliding window method), a temporal resolution of about 50 ms can be obtained resulting in a frame rate of 20 MR images per second. Although the method of S. Zhang et al. provides a sequence of MR images with a video frame rate, disadvantages with regard to the image quality may result from the sliding-window technique. In particular, image reconstruction was performed by gridding, which is a rectilinear interpolation of k-space in combination with a density compensation and inverse FFT. With this method rates of up to 20 frames per second are only obtainable when using the sliding window or fluoroscopy (S. J. Riedereret al. in “Magn. Reson. Med.” vol. 8, 1988, p. 1-15) approach, while the true temporal fidelity of the images is still determined by measuring times of 200 to 250 ms. For a repetition time of 2 ms these durations correspond to the necessary acquisition of 100 to 125 radial spokes for an image with a 128 matrix resolution.
Another approach for reducing the raw data acquisition time by undersampling the k-space is based on using a plurality of radio frequency receiver coils each providing a separate receive channel (parallel MR imaging). Radio frequency signals being excited in the field of view (FOV) are simultaneously collected with the radio frequency receiver coils. Reconstructing an MR image of the FOV from the image raw data requires a knowledge of the sensitivities (profiles) of the receiver coils. In practical MRI devices, e.g. for medical imaging, this reconstruction is based on a linear inverse method, wherein the coil sensitivities are calculated in a first step and the MR image is calculated using the fixed coil sensitivities in a subsequent second step. Parallel MR imaging with the linear inverse reconstruction provides an undersampling factor of about 2 to 3.
Recently, a nonlinear inverse method for improved autocalibrated parallel imaging has been described (M. Uecker et al. in “Magnetic resonance in medicine”, Vol. 60, 2008, p. 674-682), which combines the use of variable density trajectories with the joint estimation of image content and coil sensitivities. For this algorithm, it could also be shown that only a very small central k-space area with full sampling is required for accurate autocalibration. Both properties are particularly attractive for real-time imaging, where the coil sensitivity information has to be frequently updated to match the actual experimental situation generated by a moving object. The nonlinear inverse method yields an improved image quality and/or increased undersampling factor (about 3 to 4). However, the image reconstruction proposed by M. Uecker et al. (2008) was adapted to image raw data being generated with a gradient-echo sequence using a Cartesian k-space trajectory resulting in the drawbacks of Cartesian k-space trajectories noted above.
In order to apply a nonlinear inverse reconstruction to non-Cartesian k-space data, it has been proposed to add an interpolation step to each iteration of the algorithm (see F. Knoll et al., Poster “Improved reconstruction in non-Cartesian parallel imaging by regularized nonlinear inversion”, in “Proceedings of the 17th ISMRM scientific meeting and exhibition”, Honolulu, Hi., USA, Apr. 18-24, 2009). Although F. Knoll et al. were capable of reconstructing an MR image with an undersampling factor of about 12, the implementation of the regularized nonlinear inversion required a calculation time of about 40 s resulting in a practical application for reconstructing a single MR image only. Because such computations are rather slow, one may consider the use of a graphical processing unit (GPU) to achieve reasonable reconstruction times. A corresponding implementation for iterative SENSE (K. P. Pruessmann et al. in “Magn. Reson. Med.” vol. 42, 1999, p. 952-962) has indeed been utilized for real-time imaging (T. S. Sorensen et al. “Real-time reconstruction of sensitivity encoded radial magnetic resonance imaging using a graphics processing unit” in “IEEE Trans. Med. Imag.” vol. 28(12), 2009, p. 1974-1985). However, an efficient implementation of the interpolation algorithm on a GPU is a difficult and time-consuming task.